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arXiv · 1802.08231

Proper holomorphic mappings onto symmetric products of a Riemann surface

Gautam Bharali·Indranil Biswas·Divakaran Divakaran·Jaikrishnan Janardhanan
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Abstract

We show that the structure of proper holomorphic maps between the $n$-fold symmetric products, $n\geq 2$, of a pair of non-compact Riemann surfaces $X$ and $Y$, provided these are reasonably nice, is very rigid. Specifically, any such map is determined by a proper holomorphic map of $X$ onto $Y$. This extends existing results concerning bounded planar domains, and is a non-compact analogue of a phenomenon observed in symmetric products of compact Riemann surfaces. Along the way, we also provide a condition for the complete hyperbolicity of all $n$-fold symmetric products of a non-compact Riemann surface.

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Gautam Bharali, Indranil Biswas, Divakaran Divakaran, Jaikrishnan Janardhanan. 2018-02-22. Proper holomorphic mappings onto symmetric products of a Riemann surface. https://doi.org/10.25537/dm.2018v23.1291-1311

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